Advertisements
Advertisements
प्रश्न
If a, b, c are in continued proportion, show that: `(a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`.
उत्तर
Since a, b, c are in continued proportion,
`a/b = b/c`
`=>` b2 = ac
Now, (a2 + b2)(b2 + c2) = (a2 + ac)(ac + c2)
= a(a + c) c(a + c)
= ac(a + c)2
= b2(a + c)2
`=>` (a2 + b2)(b2 + c2) = [b(a + c)][b(a + c)]
`=> (a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`
संबंधित प्रश्न
Find the third proportional to a – b and a2 – b2
If a, b, c and dare in continued proportion, then prove that
ad (c2 + d2) = c3 (b + d)
Find the mean proportion of: `(1)/(12) and (1)/(75)`
Find the mean proportion of: (a – b) and (a³ – a²b), a> b
Show that the following numbers are in continued proportion:
36, 90, 225
4.5 g of an alloy of copper and zinc contains 3.5 g of copper. What weight of copper will there be in 18.9 g of the alloy?
If a, b, c and d are in proportion, prove that: (ma + nb) : b = (mc + nd) : d
If q is the mean proportional between p and r, prove that: p3 – 3q2 + r2 = `q^4(1/p^2 - 3/q^2 + 1/r^2)`
Find the missing number in the box in the proportions:
`8/square = 3.2/4`
There is a number in the box `square` such that `square`, 24, 9, 12 are in proportion. The number in the box is ______.
